Single-band Hubbard Model Research Articles

A galactic approach to neutron scattering science

Neutron scattering science is leading to significant advances in our understanding of materials and will be key to solving many of the challenges that society is facing today. Improvements in scientific instruments are actually making it more difficult to analyze and interpret the results of experiments due to the vast increases in the volume and complexity of data being produced and the associated computational requirements for processing that data. New approaches to enable scientists to leverage computational resources are required, and Oak Ridge National Laboratory (ORNL) has been at the forefront of developing these technologies. We recently completed the design and initial implementation of a neutrons data interpretation platform that allows seamless access to the computational resources provided by ORNL. For the first time, we have demonstrated that this platform can be used for advanced data analysis of correlated quantum materials by utilizing the world's most powerful computer system, Frontier. In particular, we have shown the end-to-end execution of the DCA++ code to determine the dynamic magnetic spin susceptibility χ(q, ω) for a single-band Hubbard model with Coulomb repulsion U/t = 8 in units of the nearest-neighbor hopping amplitude t and an electron density of n = 0.65. The following work describes the architecture, design, and implementation of the platform and how we constructed a correlated quantum materials analysis workflow to demonstrate the viability of this system to produce scientific results.

Robust correlated magnetic moments in end-modified graphene nanoribbons

We conduct a theoretical examination of the electronic and magnetic characteristics of end-modified 7-atom wide armchair graphene nanoribbons (AGNRs). Our investigation is performed within the framework of a single-band Hubbard model, beyond a mean-field approximation. First, we carry out a comprehensive comparison of various approaches for accommodating di-hydrogenation configurations at the AGNR ends. We demonstrate that the application of an on-site potential to the modified carbon atom, coupled with the addition of an electron, replicates phenomena such as the experimentally observed reduction of the bulk-states (BS) gap. These results for the density of states (DOS) and electronic densities align closely with those obtained through a method explicitly designed to account for the orbital properties of hydrogen atoms. Furthermore, our study enables a clear differentiation between magnetic moments already described in a mean-field (MF) approach, which are spatially confined to the same sites as the topological end-states (ES), and correlation-induced magnetic moments, which exhibit localization along all edges of the AGNRs. Notably, we show the robustness of these correlation-induced magnetic moments relative to end modifications, within the scope of the method we employ.

Variational Monte Carlo study of stripes as a function of doping in the t−t′ Hubbard model

We perform variational Monte Carlo simulations of the single-band Hubbard model on the square lattice with both nearest (t) and next-nearest (t′) neighbor hoppings. Our work investigates the consequences of increasing hole doping on the instauration of stripes and the behavior of the superconducting order parameter, with a discussion on how the two phenomena affect each other. We consider two different values of the next-nearest neighbor hopping parameter, that are appropriate for describing cuprate superconductors. We observe that stripes are the optimal state in a wide doping range; the stripe wavelength reduces at increasing doping, until stripes melt into a uniform state for large values of doping. Superconducting pair–pair correlations, indicating the presence of superconductivity, are always suppressed in the presence of stripes. Our results suggest that the phase diagram for the single-band Hubbard model is dominated by stripes, with superconductivity being possible only in a narrow doping range between striped states and a nonsuperconducting metal.

Active learning approach to simulations of strongly correlated matter with the ghost Gutzwiller approximation

Quantum embedding (QE) methods such as the ghost Gutzwiller approximation (gGA) offer a powerful approach to simulating strongly correlated systems, but come with the computational bottleneck of computing the ground state of an auxiliary embedding Hamiltonian (EH) iteratively. In this work, we introduce an active learning (AL) framework integrated within the gGA to address this challenge. The methodology is applied to the single-band Hubbard model and results in a significant reduction in the number of instances where the EH must be solved. Through a principal component analysis (PCA), we find that the EH parameters form a low-dimensional structure that is largely independent of the geometric specifics of the systems, especially in the strongly correlated regime. Our AL strategy enables us to discover this low-dimensionality structure on the fly, while leveraging it for reducing the computational cost of gGA, laying the groundwork for more efficient simulations of complex strongly correlated materials. Published by the American Physical Society 2024

Dynamical t/U Expansion of the Doped Hubbard Model

We construct a new U(1) slave-spin representation for the single-band Hubbard model in the large-U limit. The mean-field theory in this representation is more amenable to describe both the spin-charge-separation physics of the Mott insulator at half-filling and the strange metal behavior at finite doping. By employing a dynamical Green’s function theory for slave spins, we calculate the single-particle spectral function of electrons. The result is comparable to that in dynamical mean field theories. We then formulate a dynamical t/U expansion for the doped Hubbard model that reproduces the mean-field results at the lowest order of expansion. To the next order of expansion, it naturally yields an effective low-energy theory of a t–J model for spinons self-consistently coupled to an XXZ model for the slave spins. We show that the superexchange J is renormalized by doping, in agreement with the Gutzwiller approximation. Surprisingly, we find a new ferromagnetic channel of exchange interactions which survives in the infinite U limit, as a manifestation of the Nagaoka ferromagnetism.

Systematic determination of coupling constants in spin clusters from broken-symmetry mean-field solutions.

Quantum-chemical calculations aimed at deriving magnetic coupling constants in exchange-coupled spin clusters commonly utilize a broken-symmetry (BS) approach. This involves calculating several distinct collinear spin configurations, predominantly by density-functional theory. The energies of these configurations are interpreted in terms of the Heisenberg model, H̃=∑i<jJijs̃i⋅s̃j, to determine coupling constants Jij for spin pairs. However, this energy-based procedure has inherent limitations, primarily in its inability to provide information on isotropic spin interactions beyond those included in the Heisenberg model. Biquadratic exchange or multi-center terms, for example, are usually inaccessible and hence assumed to be negligible. The present work introduces a novel approach employing BS mean-field solutions, specifically Hartree-Fock wave functions, for the construction of effective spin Hamiltonians. This expanded method facilitates the extraction of a broader range of coupling parameters by considering not only the energies, but also Hamiltonian and overlap elements between different BS states. We demonstrate how comprehensive s=12 Hamiltonians, including multi-center terms, can be straightforwardly constructed from a complete set of BS solutions. The approach is exemplified for small clusters within the context of the half-filled single-band Hubbard model. This allows to contrast the current strategy against exact results, thereby offering an enriched understanding of the spin-Hamiltonian construction from BS solutions.

Applicability and limitations of cluster perturbation theory for Hubbard models

We present important use cases and limitations when considering results obtained from cluster perturbation theory (CPT). CPT combines the solutions of small individual clusters of an infinite lattice system with the Bloch theory of conventional band theory to provide an approximation for the Green’s function in the thermodynamic limit. To this end, we are investigating single-band and multi-band Hubbard models in 1D and 2D systems. A special interest is taken in the supposed pseudogap regime of the 2D square lattice at half-filling and intermediate interaction strength (U≤3t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U \\le 3t$$\\end{document}) as well as the metal–insulator transition. We point out that the finite-size level spacing of the cluster limits the resolution of spectral features within CPT. This restricts the investigation of asymptotic properties of the metal–insulator transition, as it would require much larger cluster sizes that are beyond computational capabilities.

Improved two-particle self-consistent approach for the single-band Hubbard model in two dimensions

Improved two-particle self-consistent approach for the single-band Hubbard model in two dimensions

Robust charge-density-wave correlations in the electron-doped single-band Hubbard model

There is growing evidence that the hole-doped single-band Hubbard and t − J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.

Optimizing Superconductivity: From Cuprates via Nickelates to Palladates.

Motivated by cuprate and nickelate superconductors, we perform a comprehensive study of the superconducting instability in the single-band Hubbard model. We calculate the spectrum and superconducting transition temperature T_{c} as a function of filling and Coulomb interaction for a range of hopping parameters, using the dynamical vertex approximation. We find the sweet spot for high T_{c} to be at intermediate coupling, moderate Fermi surface warping, and low hole doping. Combining these results with first principles calculations, neither nickelates nor cuprates are close to this optimum within the single-band description. Instead, we identify some palladates, notably RbSr_{2}PdO_{3} and A_{2}^{'}PdO_{2}Cl_{2} (A^{'}=Ba_{0.5}La_{0.5}), to be virtually optimal, while others, such as NdPdO_{2}, are too weakly correlated.

The one-dimensional Hubbard model in a magnetic field: Density profiles and ground-state phase diagram

We study the single-band one-dimensional Hubbard model in an arbitrary magnetic field using the cumulant Green's functions method (CGFM) with clusters containing 5, 6, 7, and 8 sites. We calculate the occupation numbers as functions of the chemical potential in a positive magnetic field and identify a partially filled region with negative magnetization. We obtain the ground-state phase diagram in chemical potential vs. magnetic field coordinates. We include a straightforward application of the CGFM by using a cluster as a correlated quantum dot connected to correlated leads to construct a single-electron transistor that presents a spin-polarised conductance.

The cumulant Green’s functions method for the Hubbard model

We use the cumulant Green’s functions method (CGFM) to study the single-band Hubbard model. The starting point of the method is to diagonalize a cluster (‘seed’) containing N correlated sites and employ the cumulants calculated from the cluster solution to obtain the full Green’s functions for the lattice. All calculations are done directly; no variational or self-consistent process is needed. We benchmark the one-dimensional results for the gap, the double occupancy, and the ground-state energy as functions of the electronic correlation at half-filling and the occupation numbers as functions of the chemical potential obtained from the CGFM against the corresponding results of the thermodynamic Bethe ansatz and the quantum transfer matrix methods. The particle-hole symmetry of the density of states is fulfilled, and the gap, occupation numbers, and ground-state energy tend systematically to the known results as the cluster size increases. We include a straightforward application of the CGFM to simulate the singles occupation of an optical lattice experiment with lithium-6 atoms in an eight-site Fermi-Hubbard chain near half-filling. The method can be applied to any parameter space for one, two, or three-dimensional Hubbard Hamiltonians and extended to other strongly correlated models, like the Anderson Hamiltonian, the t − J, Kondo, and Coqblin-Schrieffer models.

Accuracy of ghost rotationally invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size

We compare the accuracy of the ghost rotationally invariant slave-boson (g-RISB) theory and dynamical mean field theory (DMFT) on the single-band Hubbard model, as a function of the number of bath sites in the embedding impurity Hamiltonian. Our benchmark calculations confirm that the accuracy of g-RISB can be systematically improved by increasing the number of bath sites, similar to DMFT. With a few bath sites, we observe that g-RISB is systematically more accurate than DMFT for the ground-state observables. On the other hand, the relative accuracy of these methods is generally comparable for the quasiparticle weight and the spectral function. As expected, we observe that g-RISB satisfies the variational principle in infinite dimensions, as the total energy decreases monotonically towards the exact value as a function of the number of bath sites, suggesting that the g-RISB wave function may approach the exact ground state in infinite dimensions. Our results suggest that the g-RISB is a promising method for first-principles simulations of strongly correlated matter, which can capture the behavior of both static and dynamical observables, at a relatively low computational cost.

Hubbard Subbands and Superconductivity in the Infinite-Layer Nickelate

An effective two-dimensional two-band model for infinite-layer nickelates consists of bands obtained from $d_{x^2-y^2}$ and $s$--like orbitals. We investigate whether it could be mapped onto a single-band Hubbard model and the filling of Hubbard bands. We find that both one-band physics and a Kondo-lattice regime emerge from the same two-orbital model, depending on the strength of electronic correlations and the filling of the itinerant $s$-band. Next we investigate one-particle excitations by changing the screening. First, for weak screening the strong correlations push electrons out of the $s$-band so that the undoped nickelate is similar to a cuprate. Second, for strong screening the $s$ and $d_{x^2-y^2}$ bands are both partly filled and weakly couple. Particularly in this latter regime mapping to a one-band model gives significant spectral weight transfer between the Hubbard subbands. Finally we point out that the superconducting phases may have either $d$-wave or $s$-wave symmetry.

Formation of CuO$_2$ sublattices by suppression of interlattice correlations in tetragonal CuO

We investigate the tetragonal phase of the binary transition metal oxide CuO (t-CuO) within the context of cellular dynamical mean-field theory. Due to its strong antiferromagnetic correlations and simple structure, analysing the physics of t-CuO is of high interest as it may pave the way towards a more complete understanding of high-temperature superconductivity in hole-doped antiferromagnets. In this work we give a formal justification for the weak-coupling assumption that has previously been made for the interconnected sublattices within a single layer of t-CuO by studying the non-local self-energies of the system. We compute momentum-resolved spectral functions using a Matrix Product State (MPS)-based impurity solver directly on the real axis, which does not require any numerically ill-conditioned analytic continuation. The agreement with photoemission spectroscopy indicates that a single-band Hubbard model is sufficient to capture the material’s low energy physics. We perform calculations on a range of different temperatures, finding two magnetic regimes, for which we identify the driving mechanism behind their respective insulating state. Finally, we show that in the hole-doped regime the sublattice structure of t-CuO has interesting consequences on the symmetry of the superconducting state.

Mottness in two-dimensional van der Waals Nb3X8 monolayers (X=Cl,Br,andI)

We investigate strong electron-electron correlation effects on two-dimensional van der Waals materials ${\mathrm{Nb}}_{3}{X}_{8} (X=\mathrm{Cl},\mathrm{Br},\phantom{\rule{0.28em}{0ex}}\text{and}\phantom{\rule{0.28em}{0ex}}\mathrm{I})$. We find that the monolayers ${\mathrm{Nb}}_{3}{X}_{8}$ are ideal systems close to the strong correlation limit. They can be described by a half-filled single band Hubbard model in which the ratio between the Hubbard, $U$, and the bandwidth, $W, U/W\ensuremath{\approx}5--10$. Both Mott and magnetic transitions of the material are calculated by the slave boson mean-field theory. Doping the Mott state, a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}$ superconducting pairing instability is found. We also construct a tunable bilayer Hubbard system for two sliding ${\mathrm{Nb}}_{3}{X}_{8}$ layers. The bilayer system displays a crossover between the band insulator and Mott insulator.

Unconventional ferroelectricity in half-filling states of antiparallel stacking of twisted WSe&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;

<p indent="0mm">We report on emergence of an abnormal electronic polarization in twisted double bilayer WSe₂ in antiparallel interface stacking geometry, where local centrosymmetry of atomic registries at the twist interface does not favor the spontaneous electronic polarizations as recently observed in the parallel interface stacking geometry. The unconventional ferroelectric behaviors probed by electronic transport measurement occur at half filling insulating states at <sc>1.5 K</sc> and gradually disappear at about <sc>40 K.</sc> Single band Hubbard model based on the triangular moiré lattice and the interlayer charge transfer controlled by insulating phase transition are proposed to interpret the formation of electronic polarization states near half filling in twisted WSe₂ devices. Our work highlights the prominent role of many-body electronic interaction in fostering novel quantum states in moiré-structured systems.

Ingredients for Generalized Models of κ-Phase Organic Charge-Transfer Salts: A Review

The families of organic charge-transfer salts κ-(BEDT-TTF)2X and κ-(BETS)2X, where BEDT-TTF and BETS stand for the organic donor molecules C10H8S8 and C10H8S4Se4, respectively, and X for an inorganic electron acceptor, have been proven to serve as a powerful playground for the investigation of the physics of frustrated Mott insulators. These materials have been ascribed a model character, since the dimerization of the organic molecules allows to map these materials onto a single band Hubbard model, in which the dimers reside on an anisotropic triangular lattice. By changing the inorganic unit X or applying physical pressure, the correlation strength and anisotropy of the triangular lattice can be varied. This has led to the discovery of a variety of exotic phenomena, including quantum-spin liquid states, a plethora of long-range magnetic orders in proximity to a Mott metal-insulator transition, and unconventional superconductivity. While many of these phenomena can be described within this effective one-band Hubbard model on a triangular lattice, it has become evident in recent years that this simplified description is insufficient to capture all observed magnetic and electronic properties. The ingredients for generalized models that are relevant include, but are not limited to, spin-orbit coupling, intra-dimer charge and spin degrees of freedom, electron-lattice coupling, as well as disorder effects. Here, we review selected theoretical and experimental discoveries that clearly demonstrate the relevance thereof. At the same time, we outline that these aspects are not only relevant to this class of organic charge-transfer salts, but are also receiving increasing attention in other classes of inorganic strongly correlated electron systems. This reinforces the model character that the κ-phase organic charge-transfer salts have for understanding and discovering novel phenomena in strongly correlated electron systems from a theoretical and experimental point of view.

Consistency of potential energy in the dynamical vertex approximation

In the last decades, dynamical mean-field theory (DMFT) and its diagrammatic extensions have been successfully applied to describe local and nonlocal correlation effects in correlated electron systems. Unfortunately, except for the exact solution, it is impossible to fulfill both the Pauli principle and conservation laws at the same time. Consequently, fundamental observables such as the kinetic and potential energies are ambiguously defined. In this work, we propose an approach to overcome the ambiguity in the calculation of the potential energy within the ladder dynamical vertex approximation (D$\Gamma$A) by introducing an effective mass renormalization parameter in both the charge and the spin susceptibility of the system. We then apply our method to the half-filled single-band Hubbard model on a three-dimensional bipartite cubic lattice. We find that: (i) at weak-to-intermediate coupling, a reasonable modification of the transition temperature $\TN$ to the antiferromagnetically ordered state with respect to previous ladder D$\Gamma$A calculations without charge renormalization. This is in good agreement with dual fermion and Monte Carlo results; (ii) the renormalization of charge fluctuations in our new approach leads to a unique value for the potential energy which is substantially lower than corresponding ones from DMFT and non-self-consistent ladder D$\Gamma$A; and (iii) the hierarchy of the kinetic energies between the DMFT and the ladder D$\Gamma$A in the weak coupling regime is restored by the consideration of charge renormalization.

Screening in a two-band model for superconducting infinite-layer nickelate

Starting from an effective two-dimensional two-band model for infinite layered nickelates, consisting of bands obtained from $d$ and $s$--like orbitals, we investigate to which extend it can be mapped onto a single-band Hubbard model. We identify screening of the more itinerant $s$-like band as an important driver. In absence of screening one strongly-correlated band gives an antiferromagnetic ground state. For weak screening, the strong correlations push electrons out of the $s$-band so that the undoped nickelate remains a Mott insulator with half filled $d$ orbitals. This regime markedly differs from the observations in high-$T_c$ cuprates and pairing with $s$-wave symmetry would rather be expected in the superconducting state. In contrast, for strong screening, the $s$ and $d_{x^2-y^2}$ bands are both partly filled and couple only weakly, so that one approximately finds a self-doped $d$ band as well as tendencies towards $d$-wave pairing. Particularly in the regime of strong screening mapping to a one-band model gives interesting spectral weight transfers when a second $s$ band is also partly filled. We thus find that both one-band physics and a Kondo-lattice--like regime emerge from the same two-orbital model, depending on the strength of electronic correlations and the size of the $s$-band pocket.